document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27347>Question 27347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Triangle ABC has a right angle at A where <BR>\n" );
document.write( "AB=<BR>\n" );
document.write( "[-3] <BR>\n" );
document.write( "[ 3]<BR>\n" );
document.write( "[-2]<BR>\n" );
document.write( "and where CA= <BR>\n" );
document.write( "[-1]<BR>\n" );
document.write( "[ 3]<BR>\n" );
document.write( "[ 6]                                                               <BR>\n" );
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document.write( "{the above vectors should each be in a long square bracket}\r<BR>\n" );
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document.write( "a) Calculate the acute angle at B<BR>\n" );
document.write( "b) Find the length at AB\r<BR>\n" );
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document.write( "I have a total blank on this question. I think the acute angle at B is 45 degrees,as it's a right angle triangle, but I don't know how to prove it using the vector information given. I think i have to find BC but I am stumped on how to do that, let alone find the length of AB.\r<BR>\n" );
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document.write( "Please can you help?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15103 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Triangle ABC has a right angle at A where <BR>\n" );
document.write( "AB=....LET US REPRESENT  VECTOR AB  BY THE SYMBOL {AB}AND MODULUS OF VECTOR AB BY |AB|<BR>\n" );
document.write( "[-3] <BR>\n" );
document.write( "[ 3]<BR>\n" );
document.write( "[-2]...SO {AB}= -3I+3J-2K<BR>\n" );
document.write( "and where CA= <BR>\n" );
document.write( "[-1]<BR>\n" );
document.write( "[ 3]<BR>\n" );
document.write( "[ 6] ...SO {CA}= -1I+3J+6K...HENCE {BC}={AC}-{AB}=-{CA}-{AB}=-(-1I+3J+6K)-<BR>\n" );
document.write( "(-3I+3J-2K}=4I-6J-4K<BR>\n" );
document.write( "{BC}=4I-6J-4K\r<BR>\n" );
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document.write( "{the above vectors should each be in a long square bracket} <BR>\n" );
document.write( "a) Calculate the acute angle at B..<BR>\n" );
document.write( "LET US FIND THIS BY USING <BR>\n" );
document.write( " {AB}.{BC}=|AB|*|BC|COS(B)<BR>\n" );
document.write( "(-3I+3J-2K).(4I-6J-4K)=|-3I+3J-2K|.|4I-6J-4K|COS(B)<BR>\n" );
document.write( "-12-18+8=SQRT(9+9+4)*SQRT(16+36+16)COS(B)<BR>\n" );
document.write( "COS(B)=-22/SQRT(22*68)...THERE IS SOME THING WRONG WITH YOUR NUMBERS ..IF ANGLE B IS ACUTE WE SHOULD GET THIS AS A POSITIVE NUMBER OR LET US TAKE SQRT OF 22*68 AS -38.678.....SO THAT COS(B)=0.5688.... AND ANGLE B =0.9658 RADIANS OR 55.36 DEGREES....<BR>\n" );
document.write( "IF ANGLE A IS RIGHT ANGLE THEN WE SHOULD HAVE <BR>\n" );
document.write( " {CA}.{AB} =0...LET US CHECK..<BR>\n" );
document.write( "(-1I+3J+6K).(-3I+3J-2K)= +3+9-12=0...OK....\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "b) Find the length at AB <BR>\n" );
document.write( "WELL THIS IS |AB|= |-3I+3J-2K|=SQRT(9+9+4)=SQRT(22)=4.69\r<BR>\n" );
document.write( "\n" );
document.write( "I have a total blank on this question. I think the acute angle at B is 45 degrees,as it's a right angle triangle, but I don't know how to prove it using the vector information given. I think i have to find BC but I am stumped on how to do that, let alone find the length of AB. <BR>\n" );
document.write( "Please can you help? <BR>\n" );
document.write( "Thank you<BR>\n" );
document.write( " </SPAN>\n" );
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